We continue our study of the inverse scattering problem for diffuse light. In contrast to our earlier work, in which we considered the linear inverse problem, we now consider the nonlinear problem. We obtain a solution to this problem in the form of a functional series expansion. The first term in this expansion is the pseudoinverse of the linearized forward-scattering operator and leads to the linear inversion formulas that we have reported previously. The higher-order terms represent nonlinear corrections to this result. We illustrate our results with computer simulations in model systems.
© 2003 Optical Society of America
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.6960) Medical optics and biotechnology : Tomography
Vadim A. Markel, Joseph A. O’Sullivan, and John C. Schotland, "Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas," J. Opt. Soc. Am. A 20, 903-912 (2003)